Question

Find xif 2x (x + 2) = 4x.
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Answer 1

$\bf{2x\left(x+2\right)=4x}$

$\implies\sf{2x\left(x+2\right)-4x=4x-4x}$

$\implies\sf{2x\left(x+2\right)-4x=0}$

$\implies\sf{2x\left(2+x\right)-2\cdot \:2x=0}$

$\implies\sf{2x\left(2+x-2\right)=0}$

$\implies\sf{2x^2=0}$

$\textsf{Using\:the\:Zero\:Factor\:Principle:\quad}$

$\sf{If\:\:ab=0\:then\:a=0\:or\:b=0\:\left(or\:both\:a=0\:and\:b=0\right)}$

$\mathrm{The\:solution\:to\:the\:quadratic\:equation\:is:}$

$\boxed{\bf{\implies x=0}}$